Seeing that can be quite discouraging, but luckily, in many cases it's not too difficult to fix. As usual, there are many ways to get to a successful result, I'll describe what I consider the simplest.

What does it mean?
Dependencies are simply libraries or tools that meson needs to build the project. Usually these are declared like this in meson.build:

dep_foo = dependency('foo', version: '>= 1.1.0')

In human words: "we need the development headers for library foo (or 'libfoo') of version 1.1.0 or later". meson uses the pkg-config tool in the background to resolve that request. If we require package foo, pkg-config searches for a file foo.pc in the following directories:

/usr/lib/pkgconfig,

/usr/lib64/pkgconfig,

/usr/share/pkgconfig,

/usr/local/lib/pkgconfig,

/usr/local/share/pkgconfig

The error message simply means pkg-config couldn't find the file and you need to install the matching package from your distribution or from source.

And important note here: in most cases, we need the development headers of said library, installing just the library itself is not sufficient. After all, we're trying to build against it, not merely run against it.

What package provides the foo.pc file?

In many cases the package is the development version of the package name. Try foo-devel (Fedora, RHEL, SuSE, ...) or foo-dev (Debian, Ubuntu, ...). yum and dnf
provide a great shortcut to install any pkg-config dependency:

$> dnf install "pkgconfig(foo)"

$> yum install "pkgconfig(foo)"

will automatically search and install the right package, including its dependencies.apt-get requires a bit more effort:

My version is wrong!

Now you're stuck and you have a problem. What this means is that the package version your distribution provides is not new enough to build your software. This is where the simple solutions and and it all gets a bit more complicated - with more potential errors. Unless you are willing to go into the deep end, I recommend moving on and accepting that you can't have the newest bits on an older distribution. Because now you have to build the dependencies from source and that may then require to build their dependencies from source and before you know you've built 30 packages. If you're willing read on, otherwise - sorry, you won't be able to run your software today.

Manually installing dependencies

Now you're in the deep end, so be aware that you may see more complicated
errors in the process. First of all you need to figure out where to get the
source from. I'll now use cairo as example instead of foo so you see actual data. On rpm-based distributions like Fedora run dnf or yum:

The important field here is the URL line - got to that and you'll find the source tarballs. That should be true for most projects but you may need to google for the package name and hope. Search for the tarball with the right version number and download it. On Debian and related distributions, cairo is provided by the libcairo2-dev package. Run apt-cache show on that package:

Now to the complicated bit: In most cases, you shouldn't install the new
version over the system version because you may break other things. You're
better off installing the dependency into a custom folder ("prefix") and
point pkg-config to it. So let's say you downloaded the cairo tarball, now you need to run:

So you create a directory called dependencies and install cairo there. This
will install cairo.pc as $HOME/dependencies/lib/cairo.pc. Now all you need to do is tell pkg-config that you want it to look there as well - so you set PKG_CONFIG_PATH. If you re-run meson in the original project, pkg-config will find the new version and meson should succeed. If you have multiple packages that all require a newer version, install them into the same path and you only need to set PKG_CONFIG_PATH once. Remember you need to set PKG_CONFIG_PATH in the same shell as you are running configure from.

In the case of dependencies that use meson, you replace autotools and make with meson and ninja:

If the Version field matches what pkg-config returns, then you're set. If not, keep adjusting PKG_CONFIG_PATH until it works. There is a rare case where the Version field in the installed library doesn't match what the tarball said. That's a defective tarball and you should report this to the project, but don't worry, this hardly ever happens. In almost all cases, the cause is simply PKG_CONFIG_PATH not being set correctly. Keep trying :)

Let's assume you've managed to build the dependencies and want to run the newly built project. The only problem is: because you built against a newer library than the one on your system, you need to point it to use the new libraries.